Combine strawberries and sugar in a saucepan and place over medium heat. Once the strawberries begin to release their juices and bubble up, adjust heat to a simmer and add the lemon juice. Continue to cook at a simmer for 10-15 minutes until thick like jam, stirring every few minutes so it doesn't catch. Once it is thick enough, pour it out into a clean bowl and let it cool.

Preheat oven to 350°F. Line a 9x13-inch pan with parchment paper.

Rub sugar with lemon zest in a large bowl until it is fragrant and takes on a yellow tint. Sift in flour, baking powder, baking soda and salt and whisk until very well evenly blended.

Combine eggs, yogurt, vanilla, oil, melted butter, strawberry compote and milk in a medium bowl and whisk until completely smooth. Add food colouring if you choose to use it. Pour the wet ingredients into the bowl with dry ingredients and whisk by hand or use an electric hand mixer on low speed and beat just until combined and smooth. Do not over-mix the batter.

Spread the batter into prepared pan and dollop remaining strawberry compote randomly on top. Swirl it in with a knife and bake for 22-25 minutes until lightly golden and a skewer inserted into the center comes out clean. Transfer pan to a wire rack and let cool for 10 minutes before transferring the cake to the rack to cool completely.

For the frosting, beat cream cheese until smooth. Add just 1 tablespoon of sugar and beat again to help break down the cheese and smooth it out. Add just 2-3 tablespoon of cream and beat until smooth again. Then gradually add a bit more cream and mix until completely smooth and lump-free. Continue to gradually beat in the cream and once smooth, whip until stiff peaks. Mix in sugar and vanilla, then fold in the strawberry compote. If it is too runny after you add 1 tablespoon of the strawberry compote, then you can stop there, but otherwise, you can add the other tablespoon. Place the bowl in the fridge for 20 minutes. It will thicken up as it sits.

Spread the frosting over the cooled cake and then swirl the remaining strawberry compote over top. Serve immediately and then store in the fridge in an airtight container.